Characterization of compensators for point processes on the plane

Abstract

Given a two-parameter simple point process M, an appropriate filtration and an increasing and predictable process A satisfying some properties, we solve a martingale problem, proving the existence of a unique probability measure such that A is a compensator of M. Some examples are given, showing that the problem has no solution if the chosen filtration is too small or too large

Keywords:

• Martingale problem
• two-parameter process
• point process
• compensator
• Primary 60G55
• Secondary 60G60
• 60G48

^{*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada}

^†Research done while the second author was invited at the University of Ottawa, whom he wishes to thank for their hospitality

^{*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada}

^†Research done while the second author was invited at the University of Ottawa, whom he wishes to thank for their hospitality

Notes

^{*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada}

^†Research done while the second author was invited at the University of Ottawa, whom he wishes to thank for their hospitality